ECON6001/6701: Midterm S2 2020

ECON6001/6701: Midterm S2 2020

1   Multiple Choice Questions (30 points)

Group Q1

1. Suppose there are two consumers with the following utilities:  u1 (x) = x and u2 (x) = x .  Con- sumers’ wealth is w1  = 10 and w2  = 100. Given these utilities and wealth, which of the consumers will be more risk-averse?

(a) Consumer 1

(b) Consumer 2

(c) Both consumers will be identically risk-averse

(d) There is not enough information to determine the answer

2. Suppose there are two consumers with the following utilities:  u1 (x) = x and u2 (x) = x .  Con- sumers’ wealth is w1  = 30 and w2  = 20. Given these utilities and wealth, which of the consumers will be more risk-averse?

(a) Consumer 1

(b) Consumer 2

(c) Both consumers will be identically risk-averse

(d) There is not enough information to determine the answer

3. Suppose there are two consumers with the following utilities:  u1 (x) = x and u2 (x) = x .  Con- sumers’ wealth is w1  = 100 and w2  = 50. Given these utilities and wealth, which of the consumers will be more risk-averse?

(a) Consumer 1

(b) Consumer 2

(c) Both consumers will be identically risk-averse

(d) There is not enough information to determine the answer

Group Q2

1. Which of the statements are correct?

I. GARP can be contradicted even if SARSEU holds

II. SARSEU can be contradicted even if WARP holds

III. Rational, monotone and continuous 下 always generates choices that satisfy SARSEU

2. Which of the statements are correct?

I. GARP cannot be contradicted when SARSEU holds

II. SARSEU cannot be contradicted when WARP holds

III. Rational, monotone and continuous 下 always generates choices that contradict SARSEU

3. Which of the statements are correct?

I. GARP cannot be contradicted when SARSEU holds

II. SARSEU can be contradicted when WARP holds

III. Rational, monotone and continuous 下 may generate choices that satisfy SARSEU

Group Q3

1. Consider the following sequences of pairs:

I. x1(2)  > x2(3) , x3(3)  > x 1(1) , x2(3)  > x4(1) , x3(4)  > x2(1)

II. x2(5)  > x2(1) , x1(3)  > x5(3) , x3(2)  > x2(3)

Which of the above sequences satisfy the requirements 1-3 of SARSEU?

(a) I

(b) II

(c) Both of them

(d) None of them

2. Consider the following sequences of pairs:

I. x1(2)  > x1(3) , x3(3)  > x 1(1) , x2(1)  > x3(2) , x1(4)  > x2(4)

II. x2(5)  > x5(1) , x1(3)  > x2(3) , x3(2)  > x2(3)

Which of the above sequences satisfy the requirements 1-3 of SARSEU?

(a) I

(b) II

(c) Both of them

(d) None of them

3. Consider the following sequences of pairs:

I. x2(5)  > x5(3) , x1(3)  > x2(2) , x5(2)  > x1(5)

II. x1(2)  > x1(3) , x3(3)  > x 1(1) , x2(1)  > x3(2) , x1(4)  > x2(4)

Which of the above sequences satisfy the requirements 1-3 of SARSEU?

(a) I

(b) II

(c) Both of them

(d) None of them

Group Q4

1. Suppose S = {s1 , s2 } and a consumer evaluates AA acts as follows:

V (f) = max{X : f(s1 )(X) > 0} + min{X : f(s2 )(X) > 0}, where X denotes a prize. Consider the following acts:

What is consumer preference between this pair of acts?

(a) f 〉 g

(b) g 〉 f

(c) f ∼ g

(d) Not defined.

2. Suppose S = {s1 , s2 } and a consumer evaluates AA acts as follows:

V (f) = max{z : f(s1 )(z) > 0} + min{z : f(s2 )(z) > 0}, where z denotes a prize. Consider the following acts:

What is consumer preference between this pair of acts?

(a) f 〉 g

(b) g 〉 f

(c) f ∼ g

(d) Not defined.

3. Suppose S = {s1 , s2 } and a consumer evaluates AA acts as follows:

V (f) = max{z : f(s1 )(z) > 0} + min{z : f(s2 )(z) > 0}, where z denotes a prize. Consider the following acts:

What is consumer preference between this pair of acts?

(a) f 〉 g

(b) g 〉 f

(c) f ∼ g

(d) Not defined.

Group Q5

1. Which of the statements are correct?

I. There is no such set of priors that an MEU consumer behaves as an SEU consumer.

II. Continuous preference can be represented by a discontinuous utility.

III. An SEU consumer cannot have preference that is not rational.

2. Which of the statements are correct?

I. There exists a set of priors with which an MEU consumer behaves as an SEU consumer.

II. Continuous preference cannot be represented by a discontinuous utility.

III. An SEU consumer might have preference that is not rational.

3. Which of the statements are correct?

I. An MEU consumer’s preference is not rational.

II. Continuous preference cannot be represented by a discontinuous utility.

III. An SEU consumer cannot have preference that does not satisfy the Independence axiom.

2    Short Answer Questions (50 points)

Group Q1

1.  (12 points) Consider a consumer with u(x, y) = ^x + 2^y . What is Hicksian demand for good x?

2.  (12 points) Consider a consumer with u(x, y) = ^x + 2^y . What is Hicksian demand for good y?

Group Q2

1.  (12 points) Suppose indirect utility is v = (p北p(北)y )2 . Find syy  of the Slutsky matrix.

2.  (12 points) Suppose indirect utility is v = (p北p(北)y )3 . Find syy  of the Slutsky matrix.

Group Q3

1.  (8 points) Suppose S = {s1 , s2 } and a consumer evaluates AA acts as follows: V (f) = max{z : f(s1 )(z) > 0} + min{z : f(s2 )(z) > 0},

where z denotes a prize. Consider the following acts:

How would such agent evaluate act 0.5g + 0.5h?

2.  (8 points) Suppose S = {s1 , s2 } and a consumer evaluates AA acts as follows:

V (f) = max{z : f(s1 )(z) > 0} + min{z : f(s2 )(z) > 0},

where z denotes a prize. Consider the following acts:

How would such agent evaluate act 0.5g + 0.5h?

Group Q4

1.  (9 points) Suppose S = {s1 , s2 , s3 } and there are 3 assets available in the market with the following return vectors:  x1  = (1, 1, 1) that costs q1  = 6, x2  = (2, 0, 0) that costs q2  = 4, and x3  = (2, 1, 0) that costs q3  = 5. What would be the price of the asset with the return vector (1, 2, 1)?

2.  (9 points) Suppose S = {s1 , s2 , s3 } and there are 3 assets available in the market with the following return vectors:  x1  = (1, 1, 1) that costs q1  = 6, x2  = (0, 0, 2) that costs q2  = 6, and x3  = (2, 1, 0) that costs q3  = 5. What would be the price of the asset with the return vector (2, 1, 1)?

Group Q5

1.  (9 points) Suppose S = {s1 , s2 , s3 } and there are 3 assets available in the market with the following return vectors: x1  = (1, 1, 1), x2  = (2, 0, 0), and x3  = (2, 1, 0). A consumer wants to purchase the consumption vector (8, 6, 4) for each state. How many units of each asset will she buy?

2.  (9 points) Suppose S = {s1 , s2 , s3 } and there are 3 assets available in the market with the following return vectors: x1  = (1, 1, 1), x2  = (0, 0, 2), and x3  = (2, 1, 0). A consumer wants to purchase the consumption vector (8, 4, 6) for each state. How many units of each asset will she buy?

3   Long Answer Questions (20 points)

Version 1

Suppose a consumer’s preference is represented by the following utility function:  u(x, y) = y + (x − 1)2 .

1.  (5 points) Derive and draw ICs.

2.  (10 points) Is this preference complete?  transitive?  monotone?  continuous?  convex?  (Note that you have to justify your answer for each question.  Simply stating yes/no to each of the questions will give you no points.)

3.  (5 points) Give an example of another utility function v that represents the same preference.